Oh wow, I completely misread that. I concede my earlier statement.
No, I think at one time, early this year even, it WAS true. I remember a "threat" of disqualifying yourself for Beta status if you reapplied. But yeah, I noticed, back when I did the FFXIII registration thing, that it said "only the final application will be valid".
I had applied way back whenever the beta application first went up (For PC). I was glad I never got picked due to having a crappy PC that couldn't even run the benchmark. But now I got my new PC, I went ahead and reapplied. If I get in, woot! If not, oh well! I can hold out for another 2 months.